Group Theory methods in Physics

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Overview

This group theory is pitched at beginners at UG/PG levelso that the students can appreciate the wide applications of the group theory tools in other areas of physics     INTENDED AUDIENCE : Physics background PREREQUISITES : Linear algebra, quantum mechanics, special theory of relativity INDUSTRY SUPPORT : This tool may be applicable at R&D department of industries

Syllabus

COURSE LAYOUT Week 1 : Introduction to discrete groups, subgroups and generators, conjugacy classes Week 2 : Symmetric groups, permuation group, cycle notation Week 3 : Direct product groups, semi-direct product groups Week 4 : Symmetries of molecules, point groups and Streographic projection Week 5 : Matrix representation of groups, Reducible and irreducible representation Week 6 : Great Orthogonality Theorem and Character tables, Mulliken notation, basis Week 7 : Tensor product, projection operator, observables, selection rules, Molecular vibrations Week 8 : Continuous groups, generators, Lorentz transformations Week 9 : Orthogonal groups and Lie algebra Week 10 : Unitary groups, SU(2), SU(3), weight vector diagrams and root vector diagrams Week 11 : Wigner Eckart Theorem, Examples Week 12 : Quark model, SU(3) baryons, mesons, Wigner-Eckart theorem, hydrogen atom, dynamical symmetry